Re: Fibred toposes

[Urs Schreiber <urs.schreiber@googlemail.com>]

Dear all,

Steve Vickers wrote:

> We need to be clear what you mean by "fibred topos". I would take it as
> bounded geometric morphism E --> S, thinking of topos as generalized
> space, but Streicher has used it in a sense of functor P: X -> B that is
> the fibrational analogue of B^op -> (Topos, logical functors).

Depending on what is actually intended in the application one could
also consider variants such as B^op -> (Topos, geometric morphism) or
even such presheaves of toposes that in addition satisfy some descent
property.

Along these lines Joost Nuiten has an interesting observation in

Nuiten
Bohrification of local nets of observables
http://ncatlab.org/schreiber/show/bachelor+thesis+Nuiten

where he shows that a certain presheaf of toposes satisfying descent
by local geometric morphisms encodes certain locality structure in the
"total space" topos that is of interest in the study of local nets of
algebras.

This is probably not related to what David is looking for, but maybe
it serves as an example point in the space of interesting variants.

Best,
Urs


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]